Problem given:
14-4(2k+4) = -2(4-3k)
14-8k-16 = -8+12k
-8k-2 = -8+12k
plus 8k to each side ~~> -2 = -8+20k
plus 8 to each side ~~>6 = 20k
divide both sides by 20 ~~> 3/10 = k
Now any UTex student worth his salt knows -2(4-3k)=-8+6k
Must have been Aggie thinking here.
with that change, it becomes
14-8k-16 = -8+6k
subtracting 6k from each side
-2-14k=-8
adding two to each side
-14k=-6
k=6/14 or 3/7
Thank you.
I missed this one, too -
A yard cleanup services charges a $380 fee plus $14 per hour. Another cleanup service charges a $260 fee plus $20 per hour. How long is a job for which the two companies' costs are the same?
380+14h = 260+20h
I got this after subtracting 260 from both sides: 120+14h = 20h
What should I do next?
chargefirst=380+14h
chargesecond=260+20h
if the charges are equal, then
380+14h=260+20h
subtract 14h from both sides
380=260+6h
subtract 260 from each side
120=6h
divide by 6 both sides
h=20 hours
Thank you!
In this problem, we are given an equation:
14 - 4(2k + 4) = -2(4 - 3k)
The goal is to solve for the variable "k". To do this, we need to simplify the equation step by step using the rules of algebra.
First, let's distribute the -4 and -2 to the terms inside the parentheses:
14 - 8k - 16 = -8 + 12k
Now, let's combine like terms by adding or subtracting:
-8k - 2 = -8 + 12k
Next, we want to isolate the variable "k" on one side of the equation. To do this, we can perform addition or subtraction to move terms from one side of the equation to the other.
Let's add "8k" to both sides:
-2 + 8k = -8 + 20k
Simplifying further, we have:
8k - 2 = 20k - 8
Now, let's add "2" to both sides:
8k = 20k - 6
Since we want to solve for "k", we need to move the "20k" term to the other side of the equation. Let's subtract "20k" from both sides:
8k - 20k = -6
Simplifying further:
-12k = -6
To isolate the variable "k", we divide both sides of the equation by -12:
-12k / -12 = -6 / -12
This simplifies to:
k = 1/2
Therefore, the solution to the equation is k = 1/2.